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Question
The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m.) is:
Options
(A)`25sqrt3`
(B)`50sqrt3`
(C)`75sqrt3`
(D) 150
Solution
Let AB be the tower of height 75 m.
∠ABD = ∠ACB = 30°
Suppose C be the position of the car from the base of the tower.
In right ΔABC,
`cot 30^o=(AC)/(AB)`
`rArrAC=AB\ cot30^o`
`rArrAC=75mxxsqrt3`
`rArrAC=75sqrt3 m`
Thus, the distance of the car from the base of the tower is `75sqrt3m`.
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